We could even take an additional step on the path of honest communication and instead of "good" and "bad", say "things I like" and "things I dislike".
IMO the problem with modern political discussion (especially online) isn't vocabulary, it's lack of nuance and empathy. "Good" and "bad" are not really the problem, but rather when you only classify things are either completely good or completely bad with no middle ground.
All I'm suggesting is that we take care in our language and be up-front about subjectivity rather than mask it with objective-sounding reifications. This isn't an attack on morality nor its importance, rather it is an acknowledgment of the fact that such judgments are ultimately based on what we as individuals or as a society find acceptable or unacceptable (i.e., like or dislike). It is perfectly possible to have a strong sense of ethics without claiming that one's ethics are somehow objectively or empirically "true".
There are plenty of examples where the "right" thing to do is not pleasant, it is not socially acceptable, etc because it is instead congruent with a greater ethical structure. Please check out some moral philosophy before throwing the whole field into a bin.
"things I like" and "things I dislike" are far more honest and genuine.
Unless you're talking from a purely nihilistic viewpoint which might be rational to some extent but not really productive. "Nothing matter, nothing is wrong, nothing is right, stuff just happens". Okay but where do we go from there?
Take the following thoughts:
Killing people is a bad thing. During wars, soldiers kill people. Soldiers are virtuous people.
Do you believe/know that someone could think they believe all 3 of these things? If yes, what are their values?
Everything is situations. It's context. It's why philosophers play with so many variances of the trolley problem. Nothing is clean and easy, everyone is a hypocrite, nothing matters, stuff happens, and trying to rule a group by trying to worry about individual beliefs instead of aggregate beliefs shared among a majority (a slight difference from your statement that I took as "minimal set of shared values" which I assumed you meant applied to literally everyone).
Point is once you get a group above a certain size, there's only ever going to be majority favored ideas, not universally shared.
But, are shared values the same as good and bad? We generally consider certain forms of lying to be bad but they are not illegal. And, not everyone agrees on those. So they aren't entirely shared. If we go down the rabbit hole of reason and logic on this it's not so simple.